"There's no organisation in the world that doesn't say, 'There are some things we do that are more important than others, and those things we will not cut.' We should take the view that the Today programme is so important and has already been cut to such an extent that any more cuts will damage it.

"If continuing to fund channels like BBC3 and BBC4 means that the price to pay is that there must be damaging cuts to core programmes, then I don't believe that that is a price worth paying."

How much longer before someone sets up "Save BBC3" or "Save BBC4"? It can't be much fun at either of those two channels right now, as your BBC colleagues put you forward as a "one-stop solution" to the corporation's budgetary problems.

Humphrys paints a miserable picture of life on Today. Five years ago it had 17 reporters, now it has fewer than half that number. Pretty soon, if another 20% is lopped off its budget, it will have virtually none, he says.

"In terms of its impact and its influence on the national debate, the trust in which it is held by its huge audience, the Today programme is easily the most important programme the BBC does," argues Humphrys.

"It's all very well to say that in five years' time you will regard BBC3 and BBC4 as absolutely vital. All right, at the moment only six men and a dog watch them, but in five years' time, by God they'll be a lot more important.

"That's fine! But what if in five years' time you've damaged programmes like Today and other core programmes the BBC does? There's a real danger that we will damage those bits of the BBC that are absolutely crucial to its long-term future."

Except BBC3 has rather more viewers than six men and a dog. It's hard to believe looking at its schedule, but BBC3 has a weekly reach of 12 million viewers - around twice the weekly audience of Today - and an audience share of 2.1%, the highest of all digital channels when it is on air.

It's rather more complicated than 'which is more important - Today or BBC3?' - but there are no easy answers. And the longer it takes the corporation to come up with the solutions, the more it is going to tear itself apart.